Observational constraints on vector-like dark energy

A.-L. Y. Gschrey; C. J. A. P. Martins; C. S. C. M. Coelho

REVIEW 2 major objections 5 minor 27 references

Observational constraints on vector-like dark energy

T0 review · 2 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read Vector-field dark energy is squeezed close to LambdaCDM by low-redshift data.

desk verdict First quantitative fit of the cosmic triad to background data; the constraints are real but the phantom-prior caveat is understated in the abstract. read the letter →

arxiv 2502.04828 v1 pith:N45VOV6S submitted 2025-02-07 astro-ph.CO gr-qchep-ph

C. S. C. M. Coelho , A.-L. Y. Gschrey , C. J. A. P. Martins This is my paper · ORCID

classification astro-ph.COgr-qchep-ph PACS 95.36.+x98.80.-k

keywords vectordarkenergycosmictriadLambdaCDMequationofstatePantheonsupernovaeHubbleparameterbackgroundcosmologyphantom

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper asks whether the universe's late-time acceleration could be driven by vector fields rather than a cosmological constant or scalar fields, and it tests a specific proposal: the cosmic triad, three mutually orthogonal vector fields that together preserve isotropy. Working only with low-redshift background data—the Pantheon supernova sample in compressed form and a compilation of Hubble parameter measurements—the authors fit several subclasses of the model. They find that the model, which reduces to $\Lambda$CDM in a particular limit, is forced close to that limit: the preferred matter density and present-day dark energy equation of state match the values obtained for flat $\Lambda$CDM and $w_0$CDM with the same data, and any potential slope is constrained to be small. The choice between a power-law and an exponential potential barely matters, because the data require the potential to be nearly flat. The message is that vector-field dark energy can mimic $\Lambda$CDM, but only by being very close to it at the background level.

What carries the argument

The load-bearing object is the cosmic triad itself: three one-form vector fields pointing along mutually orthogonal spatial directions, which preserve large-scale homogeneity and isotropy at the background level while contributing density and pressure terms involving $B = \dot A + H A$ and the potential $V(A^2)$. The analysis is carried by a reparametrization in which the Proca-like equation becomes two first-order ordinary differential equations for dimensionless functions $f(z)$ and $g(z)$, with the free parameter $r = B_0/(H_0 A_0)$ controlling the present-day field speed. This parametrization yields a closed Friedmann equation whose $\Lambda$CDM limit is explicit: setting the potential slope to zero and $w_0 = -1$ recovers $E^2 = \Omega_m(1+z)^3 + (1-\Omega_m)$, and the departures from that limit are what the data constrain.

What would settle it

A direct check would be to redo the analysis on the full 1048-supernova Pantheon likelihood without binning and on a chronometer-only $H(z)$ sample, and look for shifts in the two-sigma upper limits on $n$ or $m$ and in $w_0$. If the limits move by more than the quoted uncertainties, the compression is doing real work and the 'low-redshift background data suffice' conclusion needs qualification; alternatively, future independent SN samples (e.g., DES or Roman) could push $w_0$ significantly away from $-1$, which would contradict the paper's finding.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the cosmic triad—a dark energy model built from three identical, mutually orthogonal vector fields with a self-interaction potential $V(A^2)$—is observationally viable only in the narrow regime where it behaves almost exactly like a cosmological constant. Using a four-parameter description ($\Omega_m$, $w_0$, the potential slope $n$ or $m$, and the present-day field speed ratio $r$), the authors show that the model's Friedmann equation has a well-defined $\Lambda$CDM limit at $(n=0, w_0=-1)$, and that low-redshift background data push all parameters toward that limit. Specifically, $\Omega_m = 0.27 \pm 0.02$ in the generic fits, $w_0$ is consistent with $-1$ (e.g., $-0.88^{+0.07}_{-0.08}$ under a uniform prior for the power-law potential), the potential slope is subject to an upper limit ($n < 0.42$ at two $\sigma$ in the four-parameter case), and the present-day field speed is constrained to be small, with $r$ consistent with 1 but not 0. The same data rule out the related dyad model in a flat universe, since it has no $\Lambda$CDM limit and would require substantial spatial curvature.

Load-bearing premise

The load-bearing premise is that the two background datasets, as compressed and assembled, have accurate covariances and systematics: the Pantheon sample is reduced to six correlated bins and the $H(z)$ list mixes cosmic chronometers with BAO measurements, so any bias in those compilations would shift the tight constraints on $n$, $w_0$, and $\Omega_m$.

Editorial extensions

If this is right

If the result holds, vector-field dark energy is not ruled out but is effectively indistinguishable from a cosmological constant at the background level with current low-redshift data.
The tight constraint on the potential slope means any viable cosmic triad must have an almost flat potential, so the specific power-law or exponential form of $V(A^2)$ is not separately testable with these data.
Preferred matter density and $w_0$ matching $\Lambda$CDM/$w_0$CDM means that using vector dark energy does not resolve or worsen the Hubble tension, since $H_0$ is marginalized out and results are insensitive to it.
The dyad model, lacking a $\Lambda$CDM limit, is excluded in a flat universe, implying that if a vector-based explanation is sought, the triad structure is required.
Perturbation-level predictions, including anisotropic stresses and coupled scalar-vector-tensor modes, remain untested; background constraints alone do not establish full viability.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because the constraints come from only two compressed background datasets, the tight upper limits (e.g., $n < 0.14$ in the $w_0=-1$ case) may tighten or loosen when the full Pantheon likelihood or independent SN samples like DES are used; testing this is a direct next step.
The paper's conclusion that distinguishing vector, scalar, and constant dark energy may need equivalence-principle or fine-structure tests suggests a concrete research program: combining the triad's background constraints with astrophysical tests that break the degeneracy.
The same parametrization could be extended to include perturbations or spatial curvature; the dyad's preference for a closed universe hints that curvature may change the triad constraints as well, though the paper does not test this.
If future data push $w_0$ below $-1$ while $\Omega_m$ stays near $0.27$, the uniform-prior triad fit would remain consistent, but the logarithmic-prior analysis shows the model would then have a mild preference for $\log_{10}(1+w_0) \sim -0.94$, a signature that could be checked.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Dear Colleague,

The paper delivers exactly what the title promises: observational constraints on the Armendáriz-Picón cosmic triad, using Pantheon SNe and H(z) data. As far as I can tell, this is the first time the model is fitted to modern background data rather than discussed qualitatively. The equations are internally consistent, the ΛCDM limit is recovered correctly, and the numerical parameterization is well posed. The main result—that low-redshift background data squeeze the triad close to ΛCDM—survives scrutiny, at least under the priors they adopt.

What's good: the treatment of the two potentials is symmetric and clear; the analytic marginalization over H0 is a nice touch; the paper is transparent about the datasets being taken as given and about the background-only scope. The appendix on the dyad model is a useful sanity check, even if it re-derives a known result.

Now the soft spots, in proportion.

First, the phantom-prior issue. The generic analysis in Section V imposes w0 ≥ −1, and the paper's abstract says constraints 'mildly depend' on whether phantom is allowed. That is not what Section IV shows for the constant-potential subclass: allowing phantom shifts Ωm from 0.27±0.02 to 0.34±0.04, a move of more than three quoted sigma. That is not mild, and the full model's phantom branch is never tested. So the abstract overstates the robustness. This doesn't sink the paper—the non-phantom choice is physically defensible—but it should be flagged to the authors. The claim 'fully consistent with ΛCDM' is conditional on that prior.

Second, the data compression. The six Pantheon bins and the Farooq et al. H(z) compilation mix chronometers and BAO with heterogeneous systematics. The paper takes them at face value. That's standard for a constraint paper but worth noting if the goal is precision.

Third, no code or data artifacts are provided. Exact reproduction is impossible from the text alone, though the equations are explicit enough to re-implement.

Who is this for? Model builders working on vector dark energy and anyone doing consistency tests of ΛCDM with background data. It's a solid, workmanlike constraint paper, not a paradigm shift. It deserves a serious referee—the physics is coherent, the math checks out, and the limitation is a matter of prior choice and framing, not a fatal flaw.

My recommendation: send to peer review, with a request that the authors soften the 'mildly depend' wording and, ideally, run the generic analysis without the phantom restriction to see how much the conclusions actually move.

Best regards.

Referee Report

2 major / 5 minor

Summary. This paper reports the first quantitative observational constraints on the Armendáriz-Picón cosmic-triad vector dark energy model, using the compressed Pantheon supernova sample and the 38-point H(z) compilation of Farooq et al., with H0 analytically marginalized. The authors rewrite the background Friedmann and Proca equations in dimensionless form, treat several subclasses (no potential, constant potential, r = 0, w0 = -1) and then the full model with power-law and exponential potentials. Under the priors n >= 0, m >= 0, w0 >= -1, they find Omega_m about 0.27-0.28 and w0 close to -1, with upper limits on the power-law slope (n < 0.42) and no two-sigma constraint on the exponential slope m, and conclude that low-redshift background data tightly constrain the triad to near-LambdaCDM behavior. An appendix applies the same methodology to the flat dyad model and confirms that it is ruled out unless spatial flatness is relaxed.

Significance. The paper fills a genuine gap: the cosmic-triad model has been discussed theoretically but not confronted with modern data. The numerical implementation is careful and transparent: exact analytic solutions are used where available, the LambdaCDM limit is recovered correctly in Eqs. (30) and (33), and the analytic marginalization over H0 removes dependence on the Hubble-tension scale. The comparison of two potential forms and the systematic treatment of subclasses are useful contributions. The main caveat is that the headline conclusion 'close to canonical behavior' is obtained under a prior that excludes the phantom branch, which is one of the model's distinctive features; the abstract's claim that constraints depend only mildly on whether phantom values are allowed is not demonstrated for the full model. The paper does not provide code or machine-checked proofs, but the equations are explicit and the grid-based likelihood procedure is clearly described.

major comments (2)

[Section V and Table I] The generic triad analysis is run only under the prior w0 >= -1, so the phantom region w0 < -1 is never sampled in the full four-parameter space. The abstract states that constraints 'mildly depend' on whether phantom values are allowed, but the only evidence for this statement is the constant-potential subclass of Section IV, where Eqs. (38)-(39) versus Eqs. (43)-(44) show the preferred Omega_m moving from 0.34 +/- 0.04 to 0.27 +/- 0.02. Because the triad is specifically designed to accommodate phantom behavior through n > 0 or m > 0 (see Eqs. (24)-(26) and (31)), the generic phantom case should be run (for example with a prior extending to w0 = -1.2 or lower) and the resulting posterior reported. If this is computationally expensive, the abstract and conclusions should be restricted to the w0 >= -1 prior and the prior dependence explicitly labeled as untested in the full model.
[Section VI, first paragraph] The statement that 'the preferred value of the matter density always coincides with its standard best-fit value for the same cosmological datasets' is too strong in light of the phantom-allowed constant-potential result: Eqs. (38)-(39) give Omega_m = 0.34 +/- 0.04, which is about 1.6 sigma above the w0CDM value Omega_m = 0.27 +/- 0.02 quoted in Eqs. (41)-(42). Please qualify this sentence and quantify the prior dependence in the conclusions, or modify the abstract's 'mildly depend' wording to reflect the actual shift in the central value.

minor comments (5)

[Section III] The two datasets are taken as given: the Pantheon sample is used in its six-bin compressed form and the H(z) compilation mixes cosmic chronometers with BAO measurements. Since the tight upper limits such as n < 0.14 (Eq. (50)) and m < 0.25 (Eq. (53)) depend on these compilations, a short robustness discussion (e.g., using the full Pantheon covariance or omitting the BAO H(z) points) would strengthen the claim that the constraints are not driven by compression or systematics.
[Section IV, Eq. (44)] The two-sigma limit w0 < -0.98 is reported together with the prior w0 >= -1; this is acceptable, but the posterior percentile would be clearer.
[Abstract and Section VI] The abstract says 'any deviations from this limit are constrained to be small', while Section IV says the constant-potential constraints are 'somewhat dependent' on the choice of priors. Please harmonize the wording with the numerical shift of Eqs. (38)-(44) so that the prior dependence is not downplayed.
[Section VI, last paragraph] The closing remark that distinguishing these models 'may be unfeasible if one relies only on traditional observables' is broader than what the paper demonstrates; the analysis only covers low-redshift background observables. Consider qualifying the statement to 'low-redshift background observables'.
[Appendix A, Eq. (A17)] The match condition r = -2 +/- sqrt(3 Omega_m - 2) is derived from a low-redshift expansion of E^2; adding one sentence to recall the domain of validity of this expansion would help the reader avoid overinterpreting the Omega_m >= 2/3 condition.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the triad constraints are direct fits to external low-redshift background data, and the shared-author w0CDM comparison is used only as a benchmark.

full rationale

The paper's central result is a parameter fit, not a disguised prediction: Eqs. (11)–(16) define a standard chi-square likelihood against the Pantheon and H(z) datasets, and the model equations (23)–(33) are written in terms of free parameters (Omega_m, w0, n, r) before any data are used. The claim that low-redshift background data tightly constrain the model to be close to canonical behavior (Section VI) is a posterior outcome of those fits, not an input. The only overlapping-author reference, [20] (Fernandes, Martins, and Rocha), provides w0CDM benchmark values (Omega_m = 0.27 ± 0.02, w0 = -0.92 ± 0.06) against which the triad results are compared; it is not used to derive or fix any triad parameter, so it is not load-bearing. The Section V restriction to w0 >= -1 and n >= 0 is a prior choice, and the paper itself reports in Section IV that allowing phantom values shifts Omega_m from 0.27 ± 0.02 (Eqs. 43–44) to 0.34 ± 0.04 (Eqs. 38–39); that is a prior-sensitivity caveat, not an equation-level equivalence or a fitted input renamed as a prediction. Explicit limitations, such as restricting the analysis to background observables and to flat universes, are scope statements rather than circular steps. No equation in the paper assumes the target conclusion, and no specific circular reduction can be quoted.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The paper introduces no new entities beyond the already proposed cosmic triad and dyad models. Its free parameters are the model's physical degrees of freedom, fitted to data. The main nonstandard inputs are the physically motivated priors and the two chosen potential shapes.

free parameters (5)

Omega_m (present-day matter density) = 0.27 - 0.28 for full triad; 0.34 +/- 0.04 for constant-potential special case
Fitted to the combined Pantheon + H(z) likelihood. The central claim that the model sits near LambdaCDM depends on this parameter matching the LambdaCDM value.
w0 (present-day dark energy equation of state) = -0.88 (+0.07/-0.08) to -0.93 (+0.07/-0.08) depending on potential and prior; -1.04 +/- 0.03 in constant-potential case
Fitted to data. Consistency with -1 is the main result, so this parameter carries the paper's conclusion.
n (power-law potential slope) = upper limit n < 0.14 (w0=-1 case) or n < 0.42 (generic, logarithmic prior)
Fitted; constrained to be small, supporting the near-flat potential conclusion.
m (exponential potential slope parameter) = unconstrained at 2-sigma in the generic case; upper limit m < 0.25 in the w0=-1 case
Fitted; weakly constrained, so the choice of potential hardly matters.
r (triad speed ratio B0/(H0 A0)) = r ~ 1.1 - 1.3, with asymmetric errors
Fitted; a value near 1 (zero present-day field speed) is preferred, while r=0 (decaying solution) is disfavored.

assumptions (6)

domain assumption FLRW background with zero spatial curvature
Section III: 'We will also restrict ourselves to flat universes, setting the spatial curvature parameter to zero.' If the universe is not flat, the parameter constraints shift.
domain assumption The cosmic triad field equations and energy-momentum (Eqs. 1-5) from Armendariz-Picon are correct
Section II states the equations are taken from Ref. [3] without derivation. The entire likelihood analysis is built on these equations.
ad hoc to paper The two potential forms V1 and V2 (Eqs. 6-7) cover the relevant model space
The potentials come from Refs. [3,4] and are not derived from first principles. The paper shows the constraints are insensitive to this choice.
ad hoc to paper Priors n >= 0, m >= 0, w0 >= -1 exclude no relevant physical region
Section V: 'We retain the physically safer assumptions...' Negative slopes and phantom w0 are excluded, which could in principle change the inferred limits.
domain assumption The matter Lagrangian is independent of the cosmic triad
Section II: 'one assumes that the matter Lagrangian does not depend on the cosmic triad.' A direct coupling would modify the background equations.
domain assumption The compressed Pantheon covariance and the H(z) compilation are reliable
Section III: uses six binned Pantheon points and 38 heterogeneous H(z) measurements. Systematic errors in these compilations would propagate into the quoted constraints.

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Cite this review

Pith. "Pith review of Observational constraints on vector-like dark energy." pith.science (2026). https://pith.science/paper/N45VOV6S

@misc{pith2026250204828,
  author       = {Pith},
  title        = {Pith review of: Observational constraints on vector-like dark energy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/N45VOV6S}},
  note         = {Machine review of arXiv:2502.04828}
}

abstract

The canonical cosmological model to explain the recent acceleration of the universe relies on a cosmological constant, and most dynamical dark energy and modified gravity model alternatives are based on scalar fields. Still, further alternatives are possible. One of these involves vector fields: under certain conditions, they can lead to accelerating universes while preserving large-scale homogeneity and isotropy. We report quantitative observational constraints on a model previously proposed by Armend\'ariz-Pic\'on and known as the cosmic triad. We consider several subclasses of the model, which generically is a parametric extension of the canonical $\Lambda$CDM model, as well as two possible choices of the triad's potential. Our analysis shows that any deviations from this limit are constrained to be small. In particular the preferred present-day values of the matter density and the dark energy equation of state are fully consistent with those obtained, for the same datasets, in flat $\Lambda$CDM and $w_0$CDM. The constraints mildly depend on the priors on the dark energy equation of state, specifically on whether phantom values thereof are allowed, while the choice of potential does not play a significant role since any such potential is constrained to be relatively flat.

Figures

Figures reproduced from arXiv: 2502.04828 by the authors.

**Figure 2.** Constraints on the constant potential triad model. The top panels depict the constraints on the two-dimensional [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Same as Fig. 2, excluding the possibility of phantom equations of state. Note that the Ω [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (6 more)

**Figure 4.** Figure 4: Constraints on the r = 0 triad model. The top panels depict the constraints on the two-dimensional Ωm–w0 plane: one, two and three sigma confidence levels are shown, with the colormap corresponding to the reduced chi-square. The bottom panels show the one-dimensional p…

**Figure 5.** Figure 5: Constraints on the w0 = −1 triad model with a power-law potential. The top row panels depict the constraints on the relevant two-dimensional planes: one, two and three sigma confidence levels are shown in black, with the colormap corresponding to the reduced chi-square…

**Figure 6.** Figure 6: Same as Fig. 5, for the exponential potential. [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 7.** Figure 7: Constraints on the full triad model with a power-law potential and a logarithmic prior on the dark energy equation of [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

**Figure 8.** Figure 8: Same as Fig. 7, for the exponential potential. [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

**Figure 9.** Figure 9: Regions of the (Ωm, r) parameter space in which the term in square brackets in Eq.(A15) has positive and negative values (light and dark colored regions respectively). The dotted lines correspond to r = 0 and r = ± √ 12 and the dashed ones identify r = −2 and Ωm = 2/3…

Discussion (0). Continue with ORCID to comment.

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Works this paper leans on

27 extracted references · 8 canonical work pages

[1]

Aad et al

G. Aad et al. (ATLAS), Phys. Lett. B 716, 1 (2012), arXiv:1207.7214 [hep-ex]

arXiv 2012
[2]

Chatrchyan et al

S. Chatrchyan et al. (CMS), Phys. Lett. B716, 30 (2012), arXiv:1207.7235 [hep-ex]

arXiv 2012
[3]

Armend´ ariz-Pic´ on, JCAP07, 007 (2004), arXiv:astro- ph/0405267

C. Armend´ ariz-Pic´ on, JCAP07, 007 (2004), arXiv:astro- ph/0405267

work page arXiv 2004
[4]

Rodriguez-Benites, M

C. Rodriguez-Benites, M. Gonzalez-Espinoza, G. Otal- ora, and M. Alva-Morales, Eur. Phys. J. C 84, 276 (2024), arXiv:2311.02397 [gr-qc]

arXiv 2024
[5]

Observational constraints on vector-like dark energy

has various similarities with the triad model, but also significant differences. We start in Sect. II by briefly introducing the triad model and discussing representative cosmological solu- tions for the vector field. In Sect. III we outline our numerical implementation of this model, which enables its quantitative comparison, through standard statist- ic...

work page Pith review arXiv 2025
[6]

Beltran Jimenez and A

J. Beltran Jimenez and A. L. Maroto, Phys. Rev. D 78, 063005 (2008), arXiv:0801.1486 [astro-ph]

arXiv 2008
[7]

Beltran Jimenez, R

J. Beltran Jimenez, R. Lazkoz, and A. L. Maroto, Phys. Rev. D 80, 023004 (2009), arXiv:0904.0433 [astro- ph.CO]

arXiv 2009
[8]

Instability of anisotropic cosmological solutions supported by vector fields

B. Himmetoglu, C. R. Contaldi, and M. Peloso, Phys. Rev. Lett. 102, 111301 (2009), arXiv:0809.2779 [astro- ph]

work page Pith review arXiv 2009

Show all 27 references

[9]

Esposito-Farese, C

G. Esposito-Farese, C. Pitrou, and J.-P. Uzan, Phys. Rev. D 81, 063519 (2010), arXiv:0912.0481 [gr-qc]

2010 arXiv
[10]

B. E. Meierovich, Phys. Rev. D 84, 064037 (2011), arXiv:1105.4420 [gr-qc]

2011 arXiv
[11]

Tasinato, K

G. Tasinato, K. Koyama, and N. Khosravi, JCAP 11, 037 (2013), arXiv:1307.0077 [hep-th]

2013 arXiv
[12]

Beltran Jimenez, L

J. Beltran Jimenez, L. Heisenberg, and T. S. Koivisto, JCAP 04, 046 (2016), arXiv:1602.07287 [hep-th]

2016 arXiv
[13]

Benisty, E

D. Benisty, E. I. Guendelman, A. van de Venn, D. Vasak, J. Struckmeier, and H. Stoecker, Eur. Phys. J. C 82, 264 (2022), arXiv:2109.01052 [astro-ph.CO]

2022 arXiv
[14]

G´ omez, Phys

G. G´ omez, Phys. Rev. D 107, 123535 (2023), arXiv:2202.07027 [gr-qc]

2023 arXiv
[15]

Verde, Lect

L. Verde, Lect. Notes Phys. 800, 147 (2010), arXiv:0911.3105 [astro-ph.CO]

2010 arXiv
[16]

Aghanim et al

N. Aghanim et al. (Planck), Astron. Astrophys. 641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO]

2020 arXiv
[17]

D. M. Scolnic et al. (Pan-STARRS1), Astrophys. J. 859, 101 (2018), arXiv:1710.00845 [astro-ph.CO]

2018 arXiv
[18]

A. G. Riess et al. , Astrophys. J. 853, 126 (2018), arXiv:1710.00844 [astro-ph.CO]

2018 arXiv
[19]

Farooq, F

O. Farooq, F. R. Madiyar, S. Crandall, and B. Ratra, Astrophys. J. 835, 26 (2017), arXiv:1607.03537 [astro- ph.CO]

2017 arXiv
[20]

F. K. Anagnostopoulos and S. Basilakos, Phys. Rev. D97, 063503 (2018), arXiv:1709.02356 [astro-ph.CO]

2018 arXiv
[21]

C. B. D. Fernandes, C. J. A. P. Martins, and B. A. R. Rocha, Phys. Dark Univ. 31, 100761 (2021), arXiv:2012.10513 [astro-ph.CO]

2021 arXiv
[22]

M. C. Pookkillath and K. Koyama, JCAP 10, 105 (2024), arXiv:2405.06565 [gr-qc]

2024 arXiv
[23]

T. F. Chase, M. Leizerovich, D. L´ opez Nacir, and S. Landau, (2024), arXiv:2408.12052 [astro-ph.CO]

2024 arXiv
[24]

C. M. Will, Living Rev. Rel. 17, 4 (2014), arXiv:1403.7377 [gr-qc]

2014 arXiv
[25]

C. J. A. P. Martins, Rep. Prog. Phys. 80, 126902 (2017), arXiv:1709.02923 [astro-ph.CO]

2017 arXiv
[26]

Touboul et al

P. Touboul et al. (MICROSCOPE), Phys. Rev. Lett. 129, 121102 (2022), arXiv:2209.15487 [gr-qc]

2022 arXiv
[27]

P. J. E. Peebles, Annals Phys. 447, 169159 (2022), arXiv:2208.05018 [astro-ph.CO]

2022 arXiv

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.

[1] [1]

Aad et al

G. Aad et al. (ATLAS), Phys. Lett. B 716, 1 (2012), arXiv:1207.7214 [hep-ex]

arXiv 2012

[2] [2]

Chatrchyan et al

S. Chatrchyan et al. (CMS), Phys. Lett. B716, 30 (2012), arXiv:1207.7235 [hep-ex]

arXiv 2012

[3] [3]

Armend´ ariz-Pic´ on, JCAP07, 007 (2004), arXiv:astro- ph/0405267

C. Armend´ ariz-Pic´ on, JCAP07, 007 (2004), arXiv:astro- ph/0405267

work page arXiv 2004

[4] [4]

Rodriguez-Benites, M

C. Rodriguez-Benites, M. Gonzalez-Espinoza, G. Otal- ora, and M. Alva-Morales, Eur. Phys. J. C 84, 276 (2024), arXiv:2311.02397 [gr-qc]

arXiv 2024

[5] [5]

Observational constraints on vector-like dark energy

has various similarities with the triad model, but also significant differences. We start in Sect. II by briefly introducing the triad model and discussing representative cosmological solu- tions for the vector field. In Sect. III we outline our numerical implementation of this model, which enables its quantitative comparison, through standard statist- ic...

work page Pith review arXiv 2025

[6] [6]

Beltran Jimenez and A

J. Beltran Jimenez and A. L. Maroto, Phys. Rev. D 78, 063005 (2008), arXiv:0801.1486 [astro-ph]

arXiv 2008

[7] [7]

Beltran Jimenez, R

J. Beltran Jimenez, R. Lazkoz, and A. L. Maroto, Phys. Rev. D 80, 023004 (2009), arXiv:0904.0433 [astro- ph.CO]

arXiv 2009

[8] [8]

Instability of anisotropic cosmological solutions supported by vector fields

B. Himmetoglu, C. R. Contaldi, and M. Peloso, Phys. Rev. Lett. 102, 111301 (2009), arXiv:0809.2779 [astro- ph]

work page Pith review arXiv 2009